Relativistic superconductivity in 2D: An example

Recently, we formulated an effective scalar electrodynamics model of relativistic type-II superconductivity. We discussed possible electromagnetic behaviors of superconductivity along the lines of the nonrelativistic Ginzburg–Landau theory. This brief work considers a [Formula: see text]D condensate subjected not only to a homogeneous magnetic field but also to a static radial electric field (polar coordinates). The electric field is regarded to have two components: a central constant field and a Coulomb-like field with “charge” g, where g can take only evenly spaced real numbers. We provide the single-vortex supercurrent density together with its associated magnetic flux density for the ground state of the system. Feasible extensions of this example in [Formula: see text]D curvilinear geometries could explain some superconductivity phenomena which do not occur in planar [Formula: see text]D geometries.